Ergodic properties of a generic nonintegrable quantum many-body system in the thermodynamic limit.
Ergodic properties of a generic nonintegrable quantum many-body system in the thermodynamic limit.
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热力学极限下通用不可积量子多体系统的遍历特性。
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发表时间：
1998
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通讯作者：
T. Prosen
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作者：
T. Prosen
我们研究了一种通用但简单的局部相互作用粒子的不可积量子多体系统，即一维晶格上无自旋费米子的踢参数 (t,V) 模型（相当于 1/2 自旋的踢海森堡 XX-Z 链）。动力学的统计特性（量子遍历性和量子混合）和热力学极限中量子传输的性质被认为是随着踢参数（控制不可积程度）的变化而变化的。我们发现并证明了弹道输运和非遍历、非混合动力学（意味着在所有温度下无限电导率）在零或非常小的冲击参数的可积范围内，更一般和重要的是，也在冲击参数的中间值的不可积范围内，而只有对于足够大的冲击参数，我们才能恢复量子遍历性和混合意味着正常（扩散）输运。我们提出了一个有序参数（电荷刚度 D），它控制热力学极限内从非混合和非遍历动力学（有序相，D>0）到混合和遍历动力学（无序相，D=0）的相变。此外，我们发现混合动力学范围内时间相关函数的指数衰减。结果是通过三种不同的数值和分析方法一致获得的：（i）有限系统的时间演化和时间相关函数的直接计算，（ii）有限系统的完全对角化和静态数据的统计分析，以及（iii）无限系统运动的量子不变量的代数构造，特别是时间平均可观测量。
We study a generic but simple nonintegrable quantum many-body system of locally interacting particles, namely, a kicked-parameter (t,V) model of spinless fermions on a one-dimensional lattice (equivalent to a kicked Heisenberg XX-Z chain of 1/2 spins). The statistical properties of the dynamics (quantum ergodicity and quantum mixing) and the nature of quantum transport in the thermodynamic limit are considered as the kick parameters (which control the degree of nonintegrability) are varied. We find and demonstrate ballistic transport and nonergodic, nonmixing dynamics (implying infinite conductivity at all temperatures) in the integrable regime of zero or very small kick parameters, and more generally and importantly, also in the nonintegrable regime of intermediate values of kicked parameters, whereas only for sufficiently large kick parameters do we recover quantum ergodicity and mixing implying normal (diffusive) transport. We propose an order parameter (charge stiffness D) which controls the phase transition from nonmixing and nonergodic dynamics (ordered phase, D>0) to mixing and ergodic dynamics (disordered phase, D=0) in the thermodynamic limit. Furthermore, we find exponential decay of time correlation functions in the regime of mixing dynamics. The results are obtained consistently within three different numerical and analytical approaches: (i) time evolution of a finite system and direct computation of time correlation functions, (ii) full diagonalization of finite systems and statistical analysis of stationary data, and (iii) algebraic construction of quantum invariants of motion of an infinite system, in particular the time-averaged observables.